I am currently studying Zweibach's "A First Course in String Theory" CH:9 and I have managed to understand mode expansion in the light-cone gauge, at the classical level. Right before deriving the explicit solution of the wave equation for the open string, he remarks "We will assume that we have a space-filling $D$-Brane".
In the classical sense, $D$-Branes are just hyper-surfaces that imbose Dirichlet boundary conditions at the ends of open strings. So in that sense, the existence of a space-filling $D$-Brane is equivalent to having no $D$-Branes at all. But in that case, how can we dynamically reason the existence or the significance of space-filling $D$-Branes. How does the picture change when we quantize the open string? Do we quantize the $D$-Brane, and if yes, how so? In the theory of quantized open strings, what additional features other than Dirichlet boundary conditions do space-filling $D$-Branes have?